integral from-3 to 3 of 1/((x-1)^4)

解答

\int_{- 3}^{3} \frac{1}{( x - 1 ) ^{4}} d x

发散

求解步骤

\int_{- 3}^{3} \frac{1}{( x - 1 ) ^{4}} d x

找到无定义的点（奇点）:

x = 1

如果存在

b, a < b < c, f (b) =

无定义

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 3}^{1} \frac{1}{( x - 1 ) ^{4}} d x + \int_{1}^{3} \frac{1}{( x - 1 ) ^{4}} d x

\int_{- 3}^{1} \frac{1}{( x - 1 ) ^{4}} d x =

发散

如果表达式有部分发散，则整个表达式发散

= 发散

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